At what points is the given function continuous?
-$$f ( x , y , z ) = \frac { z } { x ^ { 2 } + y ^ { 2 } - 5 }$$
A) All $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } \neq 0$
B) All $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } \neq 5$
C) All $( x , y , z )$
D) All $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } \neq 25$

Question

Quizplus · Accepted Answer

We know that a rational function is continuous at all points where the denominator is not zero.

So, for the given function to be continuous, the denominator $x^2+y^2-5$ must not be zero.

Hence, the answer is B, where we exclude all points where $x^2+y^2=5$.

At What Points Is the Given Function Continuous? - f(x,y,z)=zx2+y2−5f ( x , y , z ) = \frac { z } { x ^ { 2 } + y ^ { 2 } - 5 }f(x,y,z)=x2+y2−5z​

At What Points Is the Given Function Continuous?
- $f ( x , y , z ) = \frac { z } { x ^ { 2 } + y ^ { 2 } - 5 }$